Red Wine quality
by ##Shruti Tiwari
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This dataset of quality of the red wine consists of 13 variables and 1599 observations[1]. The first variable X is the unique identity number which I have removed in this study. Quality is the main output feature and other 11 variables are fixed.acidity, volatile.acidity, citric.acid, residual.sugar, chlorides, free.sulfur.dioxide, total.sulfur.dioxide, density, pH, sulphates, and alcohol. I have added another variable other.acid by subtracting citric.acid from fixed.acidity to study the effect of acids other than citric.acid and acetic acid. Please refer to the text file[2] for the details of these variables.
Univariate Plots Section
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The first feature of interest in univariate analysis is Quality of the red wine which is measured from 1 to 10. In this dataset the minimum quality is 3, maximum is at 8, median is 6 and mean is 5.64. The histogram of quality looks like normal distribution which is expected. But the data structure here seems to be monopolizedon average quality (5 and 6) red wine. 82.49% of the data lies in quality 5 and 6. This is definitely going to affect the outcomes of this analysis as there are very few data for higher quality and lower quality wine. Alcohol, density, sulphates, volatile acidity, fixed acidity and oher.acid have normal distributions. Chlorides and residiual.sugar looks positive skewed because of presence of far lying outliers. The histogram of total.sulfur.oxide and free.sulfur.oxide on linear scale are positively skewed structure so I plot them on log10 axis to get normalize distribution.
What is the structure of your dataset?
There are 13 variables and 1599 observations.
What is/are the main feature(s) of interest in your dataset?
Quality as an output feature is the most important feature of this dataset.
What other features in the dataset do you think will help support your investigation into your feature(s) of interest?
Alcohol, sulphates, citric.acid and volatile acidity are the main features to understand the catagorization of the red wine.
Did you create any new variables from existing variables in the dataset?
I created other.acid feature by subtracting citric.acid from fixed.acidity.
Of the features you investigated, were there any unusual distributions?
The histogram of free.sulfur.oxide and total.sulfur.oxide have positive skewed distributions. I transformed the x axis to log10 to achieve a more normalized distribution.
Did you perform any operations on the data to tidy, adjust, or change the form of the data? If so, why did you do this?
I did not have to change any data.
Bivariate Plots Section
Before starting the bivariate analysis, it would be helpful to get the idea of correlations between the variables. I plot scatterplot matrix and list the variables with significant correlations (cor. coeff. >0.2) fixed.acidity is highly correlated with density, citric acid and pH.
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Bivariate Analysis
The first and foremost plot of interest is quality vs alcohol, as the correlation between these two features is highest. I observed some outliers in the alcohol histogram which I removed for bivariate analysis. Looking at the mean of alcohol curve we observe the quality is increasing linearly with alcohol for the range between 5 to 7 while for the range 3-4 and 7-8 the mean of alcohol is constant and for the range 4-5 there is actually a decrease in the mean of alcohol. This is an interesting graph as unlike the expectations the alcohol does not have constant increase over the quality of the red wine. The outcome of the analysis of this plot is that there are other features playing significant role in the quality of the red wine. For the next plot, we study next significantly correlated relationship i.e. quality vs volatile acidity which is the amount of acetic acid in wine. The plot shows that above a threshold value higher volatile acidity decreases the quality of the wine. This relationship is linear in nature. Interestingly alcohol is also negatively correlated with volatile acidity. Now the question one may ask is how much correlation of alcohol with acetic acid constitutes the correlation of quality vs acetic acid. we will address this question in multivariate analysis section. For now our next object of interest is alcohol vs volatile.acidity plot. The smoothning method has been set at linear model(‘lm’). The plot shown negative linear correlation above a threshold acetic acid value of ~ o.4 g.dm^3. The next features correlated with quality are sulphates and citric acid.
The plot of sulphates vs quality suggests that higher content of sulphates is favourable for quality of the wine though in low quality wine the change in sulphates amount is not that evident. Similarly, the citric acid vs quality indicates that the quality of the red wine increases with increase in citric acid. This observation is expected as citric acid gives the freshness to red wine. The density of the wine is strongly correlated with alcohol and residual sugar. So, next we analyze alcohol vs density, residual sugar vs density and quality vs density. I observed an exponential decrease in alcohol with chloride so I transformed the x axis on log10 and that gives a linear decreasing relationship.
Looking at the correlation coefficient we can deduce that the pH of the red wine does not affect the quality of the red wine. The positive correlation of pH with alcohol is studied in next plots along with variation of pH with different acidity in wine. There is a slight linear increase in pH with alcohol. As alcohol is neutral solution this observation only means that wine with higher alcohol have a little less acidity than the wine with lower percentage of alcohol.
Talk about some of the relationships you observed in this part of the
investigation. How did the feature(s) of interest vary with other features in
the dataset?
In this data the main feature of the interest i.e. quality of the wine depends positively on the alcohol of the red wine.It also varies negatively with the amount of volatile.acidity or acetic.acid. The quality of the red wine improves with amount of sulphate as it is added to limit the production of acetic acid. Other than that the quality of the wine also depends on citric acid which adds freshness in the wine. ### Did you observe any interesting relationships between the other features
(not the main feature(s) of interest)? The most interesting feature in this data is positive correlation between volatile acidity and pH. As one might expect the negative correlation between the two features as pH decreases with increased acidity. My understanding is There is some lurking variable responsible for this observation that we have to figure out using multivariate analysis. Other than that alcohol depends negatively on volatile.acidity. This dependence can be explained as the presence of unwanted microbs that start decomposing alcohol in to acetic acid reducing the percentage of alcohol and increasing volatile acidity. ### What was the strongest relationship you found? The three strongest relationships are: citric.acid and acidity free.sulfur.oxide and total.sulfur.oxide quality and alcohol
Multivariate Plots Section
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Multivariate Analysis
In bivariate analysis of quality vs alcohol, we observed that in general quality is positively correlated with alcohol but there are still many data points with the high quality and low alcohol. To confirm this observation, we look at the summary of alcohol for quality= 3, 6 and 8 respectively.
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with(subset(red, quality ==3), summary(alcohol))
with(subset(red, quality ==6), summary(alcohol))
with(subset(red, quality ==8), summary(alcohol))This is evident here we can not predict the quality of the wine alone with the percentage of alcohol. So to find out the other features influencing the quality of the red wine we include the other two features correlated to quality which are sulphates(represented by the size of the data points) and citric.acid(color of the data points). The plot is in accordance with positive correlations of three features with the quality. The more darker and bigger data points for higher qualities support the observation that sulphates and citric acids are improving the quality of the wine. Still this plot lack the consistency to state that the lack of alcohol in higher qualities is compensated by high sulphates and citric acid. Therefore in this multivariate analysis we replace sulphates by volatile.acidity as the primary goal to add sulphates in wine is to keep the volatile acidity minimal. The quality variation with alcohol, volatile.acidity and citric acid does indicate the low volatile.acidity for higher quality and higher volatile acidity for lower quality. Thus we conclude that lower volatile acidity is a reliable measurement of quality of the red wine. Still, we observe many examples data points where similar proportion of alcohol/volatile.acidity/ citric acid lies in different quality, suggesting there are more features contributing to the quality of the red wine which has not been included in this dataset.
The change in density in red wine is an interplay between content of residual sugar and alcohol as can be seen in this multivariate analysis. In red wines with very low density, the content of alcohol is relatively high and that of residual sugar is low while for rather thick wines are relatively sweeter than the other wine with lower alcohol content. We gather from the data that most of the red wines (95%) have sugar content of less than 5.0 g/dm^3. Hence the change in density in red wine is caused more by the change in alcohol than change in sugar.
The most interesting analysis of this dataset is the positive correlation of volatile acidity with pH. As we observed in bivariate analysis, the pH of the red wine is increasing linearly with volatile.acidity. I suspect there is some lurking variable in play for this observation. my hypothesis is lower volatile.acidity is associated with presence of higher citric.acid or tartaric acid. This is possible if acid provides resistance to microbial infection. To study the role of citric acid in positive correlation of volatile acidity with pH. I compare the bivariate analysis of pH with volatile.acidity with and without citric.acid. We observe that for citric acid < 0.1 g.dm^3 the volatile acidity has almost no effect on pH. But we expect this relation to be negative that implies that tartaric acid is also a lurking variable in this scenario. There are no wines without tartaric acid so here we do multivariate analysis of volatile. acidity, fixed.acidity and pH. Here we observe that Higher pH corresponding to higher volatile acidity also corresponds to low fixed acidity and at fixed acidity greater than ~ 11 g/dm^3 there are no data points with pH higher than 3 and volatile acidity greater than 0.9.
Talk about some of the relationships you observed in this part of the
investigation. Were there features that strengthened each other in terms of
looking at your feature(s) of interest?
Were there any interesting or surprising interactions between features?
The interaction of volatile acidity with pH is interesting as it shows a positive correlation opposed to general expectations. The study reveals that citric acid and tartaric acid are working as lurking variables for this phenomena. It turned out to be a beautiful example of the Simpson’s paradox.
Final Plots and Summary
Plot One
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Description One
This plot shows the three main variables alcohol, citric acid and volatile acidity(acetic acid) contributing to the quality of the red wine. The plot supports that for a better quality of the red wine we need higher % of alcohol and citric acid and lower volatile acidity. Presence of some data points with nearly same proportion of alcohol, acetic acid, and citric acid lie in different quality range suggests there may be more variables which constitute significantly in making a good red wine.
Plot Two
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Description Two
Plot Three
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Description Three
I have added this plot to emphasize on the polarization of this sample. As we can see the counts of average quality is nearly 85% of all red wines. Hence any modeling for the quality of the red wine might not be true for high quality and lower quality red wines. ——
Reflection
In this analysis, I found that higher quality red wine usually tends to have higher percentage of alcohol per volume but higher quality does not ensure higher percentage of alcohol. On the other hand, higher quality do ensure lower volatile acidity(acetic acid) in wine which is often attained by higher sulphates in red wine. The dependence of citric acid on quality of the red wine is also consistent. We can safely say that higher citric acid indicates better quality of the wine but not vice-versa.
In this dataset 4 variables seem to affect the quality of the wine but apparently there are more important variables are in play which had not been included in this dataset. The Age of the wine and tannine are couple of examples.
Reference
[1] P. Cortez, A. Cerdeira, F. Almeida, T. Matos and J. Reis. Modeling wine preferences by data mining from physicochemical properties. In Decision Support Systems, Elsevier, 47(4):547-553. ISSN: 0167-9236.
[2] https://s3.amazonaws.com/udacity-hosted-downloads/ud651/wineQualityInfo.txt